The rules for exhaustion from starvation are given in the basic rules (and PHB) as:

A character needs one pound of food per day and can make food last
longer by subsisting on half rations. Eating half a pound of food in a
day counts as half a day without food.

A character can go without food for a number of days equal to 3 + his
or her Constitution modifier (minimum 1). At the end of each day
beyond that limit, a character automatically suffers one level of
exhaustion. A normal day of eating resets the count of days without
food to zero.

The second paragraph strikes me as odd, because it seems to imply that a creature with a reasonable Constitution modifier can make their rations last longer by alternately starving themselves for several days and then eating a full day's rations.1 Perhaps there are more elaborate strategies that might last even longer.

So, given the above rules and assuming I have a Constitution modifier of +0, what is the longest I can go on 10 days' rations without taking a level of exhaustion from lack of food, and what is the rationing strategy to achieve this? Assume that I have no other food source besides these rations, but my other needs (e.g. thirst) are taken care of, so making these rations last is my only concern.

1 On the other hand, maybe this isn't so odd, given that in real life, humans are evolved for survival in conditions of alternating feast and famine.

1 Answer
1

43 days

Assuming your logic is correct which it certainly seems to be by RAW. (And is discussed in this question)

Starve and Feast

The optimal rationing strategy would be to starve yourself for 3 days and then eat a full ration, resetting your count to zero. This is a cycle of 4 days. Multiply by 10 rations is 40 days and you have a days without food count of 0. Meaning you can survive 3 more days. At the end of the 44th day you will suffer exhaustion without additional food.

Half Rations

Any day you use half rations simply reduces the number of times you can reset your count by eating a full ration. Effectively costing you 3 days and only gaining 1/2 a day.